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Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

$ \displaystyle \int_{-1}^0 \frac{e^{\frac{1}{x}}}{x^3}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

03:44

Determine whether each int…

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the problem is determined. Why the agent to grow its concurrent or that wouldn't you violated those that are convergent this improper, integral but definition This is a coach is the limit. A goes to zero left hand side and each girl from next one, eh? Eat two one over X off X, you the s. Now we compute thiss definitely into girl first. Yeah, we use U substitution like you is because to wanna racks it's in you is equal to native one over x squared the axe. Now this staff meeting to grow is equal to and girl from makes you want to want over, eh? And you two wanna wise is it to you? The one over X Cube E x is equal to negative view you and this is echo two into girl from one over, eh? To make you want you You, you you Here we use my third of the integration My powers, This is Echo two Eat you you you Myers to you from one over, eh? Teo makes to want bloody would like to one and one ray dysfunction This's equal to be to make you want I'll make you one. My seat in Act one, Linus. Some shelves to one over a one or a minus. Yeah, One away. When a guy goes to their oh, from left inside, one away goes to a negative infinity. So this function goes to zero for this function. This also goes to zero. Here. Wait can use NOPD astro to compute. The limit of this function is the cultural limit of, uh we can write a lot like ice over into make your lives Axes you called one away goes to make make you infinity. Yeah, used a p D has ruled This is a culture that limit one over negative You two make you vice asked us to makes you feel better. So this's zero now Tonto Eco's tio because negative two pounds into next to one So this integral is converted Ondas awhile you is negative Two hams Ito negative one

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